To rigorously complete the proofs, we need to modify the argument in [1]}, [2]}, and [3]}. The main difference is that we need to control for the randomness in the realized contexts. For instance, concentration inequalities are used to control for the finite sample error in an expression like equation (REF ). This introduces extra terms into nearly every expression in past proofs. To keep this paper concise and focused while ensuring all claims are reproducible, we have made the complete argument available in an separate electronic companion [4]}.
